Summary of "Transistor - 3 - MOS Transistor Current Expression"
Summary of "Transistor - 3 - MOS Transistor Current Expression"
This video explains the current conduction mechanism in a MOS (Metal-Oxide-Semiconductor) transistor, focusing on how the MOS Capacitor structure is extended to a four-terminal device and how the Drain Current (I_D) is derived and behaves under different applied voltages.
Main Ideas and Concepts
- Limitation of MOS Capacitor Alone: A MOS Capacitor with an oxide layer cannot conduct current because the oxide is an insulator, preventing electron flow despite inversion charge formation.
- MOS Transistor Structure: To enable current flow, two heavily doped diffusion regions (N+ regions) are added on either side of the MOS Capacitor structure in a P-type substrate, forming the Source and Drain Terminals of the MOS Transistor.
- Doping Concentrations:
- Substrate: P-type with doping concentration \( N_A \)
- Source/Drain: N+ type with very high doping concentration \( N_D \approx 10^{17} - 10^{18} \, \text{cm}^{-3} \)
- Channel Formation and Current Flow:
- Applying a gate voltage \( V_G \) greater than the threshold voltage \( V_T \) inverts the channel, creating mobile electrons (inversion charge) under the gate oxide.
- A lateral electric field, created by applying a drain voltage \( V_D \) relative to the source (which is grounded), causes these electrons to drift from source to drain, producing a current.
- Potential Variation Along the Channel: The channel potential \( V(x) \) varies linearly from 0 at the source to \( V_D \) at the drain over the channel length \( L \). The inversion charge density at any point \( x \) depends on \( V_G - V_T - V(x) \).
- Drain Current Derivation:
- The elemental charge in a small segment \( dx \) of the channel is: \[ dQ = -C_{ox} (V_G - V_T - V(x)) \times W \, dx \]
- The Drain Current \( I_D \) is related to the drift velocity \( v \) of electrons, which is proportional to the electric field via mobility \( \mu_n \): \[ v = \mu_n E = -\mu_n \frac{dV}{dx} \]
- By integrating along the channel length, the Drain Current is obtained as: \[ I_D = \mu_n C_{ox} \frac{W}{L} \left[ (V_{GS} - V_T) V_{DS} - \frac{V_{DS}^2}{2} \right] \]
- Nature of Current: The current in the MOS channel is a drift current, not a diffusion current (unlike in a PN Junction). This explains why the current-voltage relationship is linear or quadratic rather than exponential.
- Linear and Saturation Regions:
- Linear Region: When \( V_{DS} < V_{GS} - V_T \), the current increases approximately linearly with \( V_{DS} \), and the MOSFET behaves like a voltage-controlled resistor.
- Saturation Region: When \( V_{DS} \geq V_{GS} - V_T \), the inversion charge near the drain depletes (pinch-off), causing the current to saturate and no longer increase with \( V_{DS} \). The saturation current is: \[ I_{D(sat)} = \frac{\mu_n C_{ox}}{2} \frac{W}{L} (V_{GS} - V_T)^2 \]
- Pinch-off Phenomenon: At high drain voltages, the channel near the drain "pinches off" due to insufficient inversion charge, limiting the current.
- Next Steps: The video concludes by mentioning that further analysis of \( I_D \) vs. \( V_{DS} \) and \( I_D \) vs. \( V_{GS} \) plots will be covered in the next class.
Methodology / Step-by-Step Derivation of Drain Current
- Start with MOS Capacitor structure: Metal gate, oxide layer, P-type substrate.
- Add two N+ diffusion regions: Source and Drain Terminals.
- Apply gate voltage \( V_G \) > threshold \( V_T \): Invert the channel, creating
Category
Educational
